Scientific Notation in College Algebra

Ch. P - Prerequisites

Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a compact form. It is commonly used in mathematics and science to simplify calculations and clearly indicate the scale of a number.

• Definition: A number is written in scientific notation when it is expressed as the product of a number between 1 and 10 and a power of 10.

• General Form: $a \times 10^n$, where $1 \leq |a| < 10$ and $n$ is an integer.

• Purpose: Scientific notation makes it easier to work with extremely large or small values, especially in calculations involving multiplication or division.

Example: Converting 0.000000000042 to Scientific Notation

• Step 1: Move the decimal point to the right until only one nonzero digit remains to the left of the decimal point.

• Step 2: Count the number of places the decimal point was moved. This number becomes the negative exponent of 10.

• Step 3: Write the number as a product of the new number and $10$ raised to the negative exponent.

Solution:

• Original number: 0.000000000042

• Move the decimal 11 places to the right: 4.2

• Exponent is -11 (since the decimal was moved to the right):

Scientific Notation:

$4.2 \times 10^{-11}$

Application: Scientific notation is widely used in fields such as physics, chemistry, and engineering to represent measurements like atomic sizes, distances in space, and more.